Invariant Recognition of Objects by Vision

Invariance to various transformations is key to object recognition. Image-plane invariances – such as translation, rotation and scaling – can be computed independently of the specific object. On the other hand, both invariance to rotation in depth and invariance to changes in illumination require implicit information about the 3D structure of the object or its material properties and thus more than a single “training” image. Here, we interpret same-different perceptual tasks as classification problems. This perspective allows us to provide a formal definition of the efficiency of invariance, a bias-free summary measure of the trade-off between selectivity and invariance. We believe that this definition is the most natural and should be used in physiology, psychophysics and modeling. We characterized the efficiency of invariance in a class of feedforward architectures for visual recognition that mimic the hierarchical organization of the ventral stream. We show that this class of models achieves perfect translation and scaling invariance for novel images. In this architecture a new image is represented in terms of weights of ”templates” or “basis functions” at each level in the hierarchy. Such a representation inherits the invariance of the templates, which is built in through replications of the corresponding units across positions or scales. Simulations on real images characterize the type and number of templates needed for a representation which is sufficient to support the invariant recognition of novel objects. We conclude that the templates need not be visually similar to the test objects and that using a very small number of them is sufficient for good recognition. This surprising empirical result yields intriguing implications for the learning of invariant recognition during the development of a biological organism, such as a human baby.